Bell inequalities for falsifying mesoscopic local realism via amplification of quantum noise

Macroscopic realism (MR) per se specifies that a system which has two macroscopically distinct states available to it (such as a cat being dead or alive) is at all times predetermined to be in one or other of those two states. A minimal assumption of a macroscopic realistic theory therefore is the validity of a hidden variable lambda(M) that predetermines the outcome (whether dead or alive) of a measurement (M)over-cap distinguishing the two states. Proposals to test MR generally introduce a second premise to further qualify the meaning of MR. Thus, we consider a model, macroscopic local realism (MLR), where the second premise is that measurements at one location cannot cause an instantaneous macroscopic change S to the results of measurements made on a second system at another location. To provide a practical test, we define the intermediate concept of delta-scopic local realism (delta-LR), where delta not equal 0 can be quantified, but need not be macroscopic. By considering the amplification of quantum fluctuations, we show how negation of delta-LR is possible using fields violating a continuous variable Bell inequality. A modified Bell-Clauser-Horne-Shimony-Holt inequality is derived that tests delta-LR, and a quantitative proposal given for experiments based on polarization entanglement. In the proposal, delta is the magnitude of the quantum noise scaled by an adjustable coherent amplitude a that can also be considered part of the measurement apparatus. Thus, delta is large in an absolute sense, but scales inversely with the square root of the system size, which is proportional to vertical bar alpha vertical bar(2). We discuss how the proposed experiment gives a realization of a type of Schrodinger-cat experiment without problems of decoherence.